Three dimensional through-wall imaging: Inverse scattering problems with an inhomogeneous background medium

This paper investigates the three dimensional inverse scattering problem with an inhomogeneous background medium where the known inhomogeneities are bounded in a finite domain. The forward scattering problem is solved using the finite element-boundary integral method (FEM-BI) while the inverse problem is oriented to minimize a cost function using nonlinear conjugate gradient optimization algorithm. The background Green's function at each discrete point on the surface of the computational domain can be numerically obtained using commercial software. Such an approach shrinks the domain of inversion to a much smaller region than the standard finite difference approach. The algorithm presented in this paper finds wide applications in nondestructive evaluation, such as through-wall imaging.